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On the Boundary of Self-Affine Sets

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  • Qi-Rong Deng
  • Xiang-Yang Wang

Abstract

This paper is devoted to studying the boundary behavior of self-affine sets. We prove that the boundary of an integral self-affine set has Lebesgue measure zero. In addition, we consider the variety of the boundary of a self-affine set when some other contractive maps are added. We show that the complexity of the boundary of the new self-affine set may be the same, more complex, or simpler; any one of the three cases is possible.

Suggested Citation

  • Qi-Rong Deng & Xiang-Yang Wang, 2015. "On the Boundary of Self-Affine Sets," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-3, February.
    • Handle: RePEc:hin:jnlaaa:573604
    DOI: 10.1155/2015/573604
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